When formulating three-dimensional \({\cal N}\) -extended conformal supergravity in conformal superspace [1]}, all information
about the corresponding superspace geometry is encoded in a single curvature superfield, which is the super-Cotton
tensor \({\cal W}\) .
The functional structure of the super-Cotton tensor is \({\cal N}\) -dependent.
The \({\cal N}=1\)  super-Cotton tensor [2]}
is a primary symmetric rank-3 spinor superfield
\({\cal W}_{\alpha \beta \gamma }\)  of dimension 5/2, which obeys the conformally invariant constraint
[1]}
\(\nabla ^\alpha {\cal W}_{\alpha \beta \gamma } = 0 ~.\) 
